Constant rank-type constraint qualifications and second-order optimality conditions

• Ano de defesa: 2023
• Autor(a) principal: Silveira, Thiago Parente da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Condição de qualificação; Condições de otimalidade de segunda ordem; Constant rank; Constraint qualification; Posto constante; Programação sob o cone de segunda ordem; Second-order cone programming; Second-order optimality conditions
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-27122023-192122/

The constant rank constraint qualification, introduced by Janin in [Math. Program. Study 21:110-126, 1984], has been shown very robust in diverse applications, such as global convergence of algorithms, second-order optimality conditions, computing the derivative of the value function, and stability analysis, but always in the nonlinear programming context. In this thesis, we propose different approaches to defining a constant rank-type constraint qualification for nonlinear second-order cone programming problems, that may be based either on the sequential optimality condition and then provide global convergence of an augmented Lagrangian algorithm, or a sequential approach based on the eigenvectors structure of the second-order cone and then get global convergence of algorithms based on an external penalty method, or a classical approach based on a constant rank theorem and then guarantees second-order necessary optimality condition based on the critical cone and holds for any Lagrange multiplier.